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a=\(\dfrac{1}{2}\cdot\dfrac{3}{4}\cdot\dfrac{5}{6}\cdot\dfrac{7}{8}\cdot...\cdot\dfrac{79}{80}\)
a<\(\dfrac{2}{3}\cdot\dfrac{4}{5}\cdot\dfrac{6}{7}\cdot\dfrac{8}{9}\cdot...\cdot\dfrac{80}{81}\)
\(\text{a}^2< \dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot\dfrac{5}{6}\cdot\dfrac{6}{7}\cdot\dfrac{7}{8}\cdot\dfrac{8}{9}\cdot...\cdot\dfrac{79}{80}\cdot\dfrac{80}{81}\)
\(\Rightarrow\text{a}^2< \dfrac{1}{81}=\left(\dfrac{1}{9}\right)^2\)
\(\Rightarrow\text{a}< \dfrac{1}{9}\)(dpcm)
Nho tich cho mk nhe
A = \(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}.....\dfrac{79}{80}\)
=> A1 < \(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{5}{6}.....\dfrac{80}{81}\)
=> A2 < A.A1 = \(\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}....\dfrac{79}{80}.\dfrac{80}{81}=\dfrac{1}{81}=\left(\dfrac{1}{9}\right)^2\)
=> A < \(\dfrac{1}{9}.\)
9: \(=1-\dfrac{1}{99}+1-\dfrac{1}{100}+\dfrac{100}{101}\cdot\dfrac{1-4+3}{12}=2-\dfrac{199}{9900}=\dfrac{19601}{9900}\)
10: \(=\left(\dfrac{78}{79}+\dfrac{79}{80}+\dfrac{80}{81}\right)\cdot\dfrac{6+5+9-20}{30}=0\)
C = 3/4 + 8/9 + 15/16 + ... + 9999/10000
C = 1- 1/4 + 1- 1/9 + 1- 1/16 + ... + 1- 1/10000
C = ( 1+1+1+...+1) - (1/2.2 + 1/3.3 + 1/4.4 + ...+ 1/100.100) >
(1+1+1+...+1) - ( 1/1.2+1/2.3+1/3.4+...+1/99.100) = 99 - ( 1/1-1/2+1/2-1/3+1/3+1/4+...+1/9999-1/10000
= 99 - ( 1-1/10000)= 99 - 1 + 1/10000= 98+1/10000 > 98
Vậy C > 98
1,
x =( -12 . ( -3) ) : 2
x = 18
2,
a, -7/9 . 6/11 + (-2/9) = -14/33 + (-2/9) = -64/99
b, -4/7 : 2 = -4/7 . 1/2 = -2/7
c, 115 - (24 - 5. 3) = 115 - ( 24 - 15) = 115 - 9 = 106
d,= -3/7. (5/9 + 4/9) + 17/7 = -3/7 . 1 +17/7 = -3/7 . 17/7 = -51/49
e, ??? mình cx k biết
có bị sai đề không đấy bạn
CMR A> 1/9 thì mới làm được chứ